A note on spontaneous symmetry breaking in the mean-field Bose gas

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2025年10月14日

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Andreas Deuchert,
Phan Thành Nam,
Marcin Napiórkowski

摘要

We consider the homogeneous Bose gas in the three-dimensional unit torus, where N particles interact via a two-body potential of the form $N^{-1} v(x)$ $N^{- 1} v (x)$ . The system is studied at inverse temperatures of order $N^{-2/3}$ $N^{- 2 / 3}$ , which corresponds to the temperature scale of the Bose–Einstein condensation phase transition. We show that spontaneous U(1) symmetry breaking occurs if and only if the system exhibits Bose–Einstein condensation in the sense that the one-particle density matrix of the Gibbs state has a macroscopic eigenvalue.